Isabella wants to tile the floor of her square kitchen with square tiles that have length 20 centimeters. If the length of her kitchen is seven meters, how many tiles does she need?
There are several ways of approaching this problem. One way would be to calculate the area of the kitchen, also calculate the area of each tile, and divide these values. We notice that our units here are different. The tiles are measured in centimeters and the kitchen in meters. There are 100 centimeters in one meter. Therefore, the length of the kitchen is 700 centimeters.
We recall that the area of any square is equal to the side length squared. The area of the kitchen in square centimeters is therefore equal to 700 squared. Squaring a number involves multiplying it by itself. As seven multiplied by seven is 49, 700 multiplied by 700 is 490000. We have four zeros. The area of the kitchen is therefore equal to 490000 square centimeters.
We can calculate the area of one tile by squaring 20 as each tile has length 20 centimeters. 20 squared is equal to 400. Therefore, the area of one tile is 400 square centimeters. As both of our units are the same, we can now calculate the number of tiles by dividing 490000 by 400. This fraction can be simplified by dividing the numerator and denominator by 100. This leaves us with 4900 divided by four.
We can work out 4900 divided by four using the short division bus stop method. Four divided by four is equal to one. Nine divided by four is equal to two remainder one. 10 divided by four is equal to two remainder two. Finally, 20 divided by four is equal to five. 4900 divided by four is equal to 1225. This means that Isabella requires 1225 tiles to cover the kitchen floor.
An alternative method here would be to work out how many tiles are required along the length first. To do this, we would divide 700 by 20. This is the same as 70 divided by two, which is equal to 35. As 35 tiles would be required along each length, the total number of tiles would be equal to 35 squared. Once again, this is equal to 1225.